Commutative affine rings
type: Item
instance of: scholarly article
title: Commutative affine rings
zbMATH Open document ID: 0941.16003
DOI: 10.1007/BF02674285
published in: Siberian Mathematical Journal
publication date: 2000-04-16T00:00:00Z
review text: The semidirect extension of the automorphism group \(\Aut_RR\), where \(R\) is an associative ring with unity, by the additive group \(R^+\) is called the affine group of the ring \(R\) and denoted by \(\text{Aff}_RR\). The author discusses the question of determining a ring \(R\) from its affine group \(\text{Aff}_RR\) in the category of \(R\)-modules. He calls a module \(_RM\) over a commutative ring \(R\) an \(E\)-module if \(\text{Hom}_\mathbb{Z}(R,M)=\text{Hom}_R(R,M)\). A ring \(R\) is called an \(E\)-ring if \(_RR\) is an \(E\)-module. The author obtains some conditions sufficient for an \(E\)-ring to be an affine ring.
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 20K15
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 13B10
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 1432164
zbMATH Keywords: affine groups of rings
zbMATH Keywords: affine \(E\)-rings
zbMATH Keywords: automorphism groups of rings
zbMATH Keywords: additive groups of rings
zbMATH Keywords: categories of modules
zbMATH Keywords: \(E\)-modules
author: I. Kh. Bekker
MaRDI profile type: Publication
cites work: Q5182382
cites work: Q3281123
cites work: Q4729977
cites work: Large E-rings exist
cites work: Semiperfect Prüfer rings and FPF rings
cites work: Torsion-free E-modules
description: scientific article; zbMATH DE number 1432164